Do you need some help in preparing for your upcoming Maths exam? We’ve compiled a list of MCQ Questions for Class 12 Maths with Answers to get you started with the subject, Linear Programming Class 12 MCQs Questions with Answers. You can download NCERT MCQ Questions for Class 12 Maths Chapter 12 Linear Programming with Answers Pdf free download and learn how smart students improve problem-solving skills well ahead. So, ace up your preparation with Class 12 Maths Chapter 12 Linear Programming Objective Questions.

## Linear Programming Class 12 MCQs Questions with Answers

Don’t forget to practice the multitude of MCQ Questions on Linear Programming Class 12 with answers so you can apply your skills during the exam.

Question 1.

The point which does not lie in the half plane 2x + 3y -12 < 0 is

(a) (1, 2)

(b) (2, 1)

(c) (2, 3)

(d) (-3, 2).

## Answer

Answer: (c) (2, 3)

Hint:

Putting (2, 3) in 2x + 3y – 12.

Which becomes:

2(2)+ 3(3) – 12 = 4 + 9 – 12 = 1 > 0 and not ≤ 0.

Question 2.

The corner points of the feasible region determined by the following system of linear inequalities:

2x + y ≤ 10, x + 3y ≤ 15, x, y ≥ 0 are (0, 0), (5, 0), (3, 4) and (0, 5).

Let Z = px + qy, where p, q > 0. Conditions on p and q so that the maximum of Z occurs at both (3, 4) and (0, 5) is

(a) p = 3q

(b) p = 2q

(c) p = q

(d) q = 3p.

## Answer

Answer: (d) q = 3p.

Question 3.

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q > 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is

(a) p = q

(b) p = 2q

(c) q = 2p

(d) q = 3p.

## Answer

Answer: (d) q = 3p.

Question 4.

The feasible solution for a LPP is shown in the following figure. Let Z = 3x – 4y be the objective function.

Minimum of Z occurs at:

(a) (0, 0)

(b) (0, 8)

(c) (5, 0)

(d) (4, 10).

## Answer

Answer: (b) (0, 8)

Question 5.

The corner points of the feasible region determined by the system of linear constraints are (0, 10), (5, 5), (15, 15), (0, 20). Let Z = px + qy, where p, q> 0. Condition on p and q so that the maximum of Z occurs at both the points (15, 15) and (0, 20) is Maximum of Z occurs at:

(a) (5, 0)

(b) (6, 5)

(c) (6, 8)

(d) (4, 10).

## Answer

Answer: (a) (5, 0)

Fill in the Blanks

Question 1.

Maximum of Z = x + 2y subject to

x + y ≥ 5, x ≥ 0, y ≥ 0 is …………….. at …………….

## Answer

Answer: 10, (0,5).

Question 2.

Minimum of Z = x + y subject to:

2x + y ≥ 3, x + 2y ≥ 6, x ≥ 0, y ≥ 0 is ………………. at …………….

## Answer

Answer: 3, (0.3).

Question 3.

Maximum and Minimum of Z = 3x + 4 v ≤ 80 subject to 3x + 4v ≤ 80, x + 3y ≤ 30, x ≥ 0, y ≥ 0 are …………….. and …………….

## Answer

Answer: 21600, 0.

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